Summary: AE_Tutorial 12 gives the design problems on Audio & Radio Frequency Oscillators.

**AE_Tutorial 12. Problems on OSCILLATORS**

Problems have been taken from:

“Microelectronic Circuit Design” by R.C.Jaeger and T.N. Blalock, 2^{nd} Edition, McGraw Hill,2006.

“Microelectronic Circuits- Analysis & Design”, Muhammad H. Rashid, Thomson, Indian Edition, 1999.

*Problem (1)Wien Bridge Oscillator*

This is called Diode amplitude stabilization of a Wien Bridge Oscillator.

Determine frequency of oscillation & the amplitude of the oscillation.

[Ans:- 9.95 kHz,3.0V]

When the diodes are off,the gain of the amplifier is

So that loop gain >1 and the oscillations grow.

When diode turn ON, the gain is

PROBLEM(2)

Design the Colpitt’s for oscillation frequency

Step(1) Choose

Step(2) Calculate L from

Step(3) Calculate R_{F} & R_{L}.

Let R_{L}=100kΩ Therefore R_{F}=

Step(4) Determine R_{1}______Let A=10

Step(5) Determmine g_{m}

PROBLEM(3) Colpitts Oscillator Using BJT

Calculate (i) Frequency of oscillation.

(ii)Check the Barkhausen criteria.

(iii)Determine R_{2}.

Solution:-

RFC acts as a open circuit And C_{B} and C_{E} acts as a short circuit.

Therefore the Equivalent Circuit is :-

From the nodal equations we get equating the imaginary parts

Equating Real parts we get

For large values of

Gain

Subs

For

Sub (4) in (3)

(i)This

(ii)Frequency of oscillation=

(iii)

PROBLEM(4)LC-Tuned MOS Oscillator

Design an oscillator at

For oscillation Loop Gain= 1∠0˚

Step(1) Choose a suitable value of C:

Let C=0.01μF

Step(2) Calculate the value of L from

Step(3) Find the value of R_{1} from Eq

Step(4)

PROBLEM(5)

Design a Hartley Oscillator at f_{o}=5MHz.USE 2N3822 n-JFET whose parameters are

Load Resistance is R_{L}=100Ω

The circuit is:-

Practically it is implemented in the following manner:-

The incremental circuit is given in Figure 10.

Solution:-

BY analysis:-

We take

PROBLEM(6)CRYSTAL OSCILLATOR

This is a Colpitts-derived op-amp crystal oscillator which uses crystal as an inductor.

This uses a 2 MHz crystal oscillator

Find the frequency of oscillator.

Given

Equivalent Circuit of Crystal Oscillator:

This can also be expressed as:

Effective Capacitance C_{eq} is parallel with

It is given that 2MHz crystal is used. Hence the result is self consistent.

This is the frequency of the Crystal Oscillator.